Related papers: From Krylov Complexity to Observability: Capturing…
Quantum complexity measures the difficulty of obtaining a given state starting from a typically unentangled state. In this work, we show that complexity, when defined through the minimization of a Riemannian cost functional over the…
Scrambling quantum systems have attracted attention as effective substrates for temporal information processing. Here we consider a quantum reservoir processing framework that captures a broad range of physical computing models with quantum…
The difficulty to simulate the dynamics of open quantum systems resides in their coupling to many-body reservoirs with exponentially large Hilbert space. Applying a tensor network approach in the time domain, we demonstrate that effective…
Several Krylov-type procedures are introduced that generalize matrix Krylov methods for tensor computations. They are denoted minimal Krylov recursion, maximal Krylov recursion, contracted tensor product Krylov recursion. It is proved that…
Recently, the propagation of information through quantum many-body systems, developed to study quantum chaos, have found many application from black holes to disordered spin systems. Among other quantitative tools, Krylov complexity has…
A reservoir computer is a complex dynamical system, often created by coupling nonlinear nodes in a network. The nodes are all driven by a common driving signal. In this work, three dimension estimation methods, false nearest neighbor,…
Quantum Reservoir Computing (QRC) leverages quantum systems to perform complex computational tasks with exceptional efficiency and reduced energy consumption. We introduce a minimalistic QRC framework utilizing as few as five atoms in a…
We establish a direct correspondence between Krylov and Nielsen complexity by choosing the Krylov basis to be part of the elementary gate set of Nielsen geometry and selecting a Nielsen complexity metric compatible with the Krylov metric.…
An a posteriori estimate for the error of a standard Krylov approximation to the matrix exponential is derived. The estimate is based on the defect (residual) of the Krylov approximation and is proven to constitute a rigorous upper bound on…
Reservoir Computing is an emerging machine learning framework which is a versatile option for utilising physical systems for computation. In this paper, we demonstrate how a single node reservoir, made of a simple electronic circuit, can be…
We address the problem of sensing the curvature of a manifold by performing measurements on a particle constrained to the manifold itself. In particular, we consider situations where the dynamics of the particle is quantum mechanical and…
The rapid development of machine learning and quantum computing has placed quantum machine learning at the forefront of research. However, existing quantum machine learning algorithms based on quantum variational algorithms face challenges…
Quantum operator scrambling describes the spreading of local operators into the whole system in the picture of Heisenberg evolution, which is often quantified by the operator size growth. Here we propose a measure of quantum operator…
One often wishes for the ability to formally analyze large-scale systems---typically, however, one can either formally analyze a rather small system or informally analyze a large-scale system. This work tries to further close this…
We propose a measure of quantum state complexity defined by minimizing the spread of the wave-function over all choices of basis. Our measure is controlled by the "survival amplitude" for a state to remain unchanged, and can be efficiently…
Introductory state-space linear control courses focus on linear, time-invariant systems and spend intense efforts by introducing system realizations that allow the student to grasp fundamental concepts, among which controllability,…
We consider a number of aspects of the problem of defining time observables in quantum theory. Time observables are interesting quantities in quantum theory because they often cannot be associated with self-adjoint operators. Their…
Quantum reservoir computing is a machine learning framework that offers ease of training compared to other quantum neural networks, as it does not rely on gradient-based optimization. Learning is performed in a single step on the output…
Reservoir computing is a framework which is primarily used for temporal information processing, using the intrinsic dynamics of an underlying physical system. The framework, in a quantum setup, is implemented using ergodic dynamics…
A rich variety of non-equilibrium dynamical phenomena and processes unambiguously calls for the development of general numerical techniques to probe and estimate a complex interplay between spatial and temporal degrees of freedom in…